Answer: To solve the inequality x^2 - 8x + 15 < 0, we first want to find the critical points, which are the points where the quadratic function changes direction (from increasing to decreasing or vice versa). To find the critical points, we need to set the quadratic equal to zero and solve for x. In this case, we have:
x^2 - 8x + 15 = 0
To solve this equation we should factor it or use the quadratic formula.
(x - 5)(x - 3) = 0
x = 5, x = 3
This means that the critical points for the inequality are x = 5 and x = 3. To find the solution set of the inequality, we test the signs of the function at the critical points and in the intervals between them.
The solution of the inequality is x < 3 or x > 5.
Explanation: